initial.py

class GMM:
    """ Gaussian Mixture Model
    
    Parameters
    -----------
        k: int , number of gaussian distributions
        
        seed: int, will be randomly set if None
        
        max_iter: int, number of iterations to run algorithm, default: 200
        
    Attributes
    -----------
       centroids: array, k, number_features
       
       cluster_labels: label for each data point
       
    """
    def __init__(self, C, n_runs):
        self.C = C # number of Guassians/clusters
        self.n_runs = n_runs
        
    
    def get_params(self):
        return (self.mu, self.pi, self.sigma)
    
    
        
    def calculate_mean_covariance(self, X, prediction):
        """Calculate means and covariance of different
            clusters from k-means prediction
        
        Parameters:
        ------------
        prediction: cluster labels from k-means
        
        X: N*d numpy array data points 
        
        Returns:
        -------------
        intial_means: for E-step of EM algorithm
        
        intial_cov: for E-step of EM algorithm
        
        """
        d = X.shape[1]
        labels = np.unique(prediction)
        self.initial_means = np.zeros((self.C, d))
        self.initial_cov = np.zeros((self.C, d, d))
        self.initial_pi = np.zeros(self.C)
        
        counter=0
        for label in labels:
            ids = np.where(prediction == label) # returns indices
            self.initial_pi[counter] = len(ids[0]) / X.shape[0]
            self.initial_means[counter,:] = np.mean(X[ids], axis = 0)
            de_meaned = X[ids] - self.initial_means[counter,:]
            Nk = X[ids].shape[0] # number of data points in current gaussian
            self.initial_cov[counter,:, :] = np.dot(self.initial_pi[counter] * de_meaned.T, de_meaned) / Nk
            counter+=1
        assert np.sum(self.initial_pi) == 1    
            
        return (self.initial_means, self.initial_cov, self.initial_pi)